Answer:
60 degrees
Step-by-step explanation:
A triangle adds up to 180 degrees. 180 divided by 3 is 60. The answer is 60 degrees.
Since segment AC bisects (aka cuts in half) angle A, this means the two angles CAB and CAD are the same measure. I'll refer to this later as "fact 1".
Triangles ABC and ADC have the shared segment AC between them. By the reflexive property AC = AC. Any segment is equal in length to itself. I'll call this "fact 2" later on.
Similar to fact 1, we have angle ACB = angle ACD. This is because AC bisects angle BCD into two smaller equal halves. I'll call this fact 3
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To summarize so far, we have these three facts
- angle CAB = angle CAD
- AC = AC
- angle ACB = angle ACD
in this exact order, we can use the ASA (angle side angle) congruence property to prove the two triangles are congruent. Facts 1 and 3 refer to the "A" parts of "ASA", while fact 2 refers to the "S" of "ASA". The order matters. Notice how the side is between the angles in question.
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Once we prove the triangles are congruent, we use CPCTC (corresponding parts of congruent triangles are congruent) to conclude that AB = AD and BC = BD. These pair of sides correspond, so they must be congruent in order for the entire triangles to be congruent overall.
It's like saying you had 2 identical houses, so the front doors must be the same. The houses are the triangles (the larger structure) and the door is an analogy to the sides (which are pieces of the larger structure).
Answer:
x=500
Step-by-step explanation:
Solve the equation by rewriting in exponential form using the definition of a logarithm and simplifying.
x
=500
Answer:
Volume of cylinder is 34833.21 ft³
Step-by-step explanation:
Given : A right circular cylinder having height 
ft and diameter 
times its height.
Given : diameter times its height that is
diameter times that is
Diameter = 
Diameter = 
ft
Radius is half of diameter,
Radius = 
ft
Substitute the values, we get,
Thus, volume of cylinder is 34833.21 ft³
